The image shows a rectangular prism for which the surface area and volume are to be calculated. Let's go through each step for solving this:

Step 1: Volume Calculation

The volume $V$ of a rectangular prism is given by the formula:

$V = \text{length} \times \text{width} \times \text{height}$

From the image, the dimensions are:

• Length = $6 \, \text{cm}$
• Width = $3 \, \text{cm}$
• Height = $2 \, \text{cm}$

Substituting the values:

$V = 6 \times 3 \times 2 = 36 \, \text{cm}^3$

Step 2: Surface Area Calculation

The surface area $A$ of a rectangular prism is the sum of the areas of all six faces. The formula is:

$A = 2(\text{length} \times \text{width} + \text{width} \times \text{height} + \text{length} \times \text{height})$

Substitute the dimensions: $A = 2(6 \times 3 + 3 \times 2 + 6 \times 2)$ $A = 2(18 + 6 + 12) = 2 \times 36 = 72 \, \text{cm}^2$

Final Answer:

• Surface Area = $72 \, \text{cm}^2$
• Volume = $36 \, \text{cm}^3$

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How does changing the height of the prism affect its volume and surface area?
2. What is the difference between surface area and volume in practical terms?
3. How would you calculate the surface area of an irregular shape?
4. Can two different prisms have the same volume but different surface areas?
5. How can you use the volume formula to calculate the capacity of a container?

Tip: When calculating the surface area of a prism, always remember that it has three pairs of identical faces. This simplifies the calculation!